Would anyone be able to help me with a proof. The question is:

Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x+2
Let A={g Є C[0,1]: d(g,f) > 3}. Prove that A is an open set
Let B={g Є C[0,1]: 1 ≤ d(g,f) ≤ 3}. Prove that B is a closed set

Any help or suggestions would really be appreciated.